Volume of a Cylinder Examples: 21 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Volume of a Cylinder.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The amount of three-dimensional space inside a cylinder, found by multiplying the area of the circular base by the height.

Imagine stacking hundreds of identical circular coins into a tall tower. Each coin is a thin circle with area $\pi r^2$ , and stacking $h$ units high gives you a cylinder. The volume is just the area of one coin times the height of the stack.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Cylinder volume is base area repeated through height.

Common stuck point: The procedure for volume of a cylinder is the easy part; the trap is using $2\pi r$ instead of $\pi r^2$ for the base. Asking "Can I identify the circular base area and the height?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Can I identify the circular base area and the height?

Worked Examples

Example 1

easy

A cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. Use

\pi \approx 3.14

Find the volume of this cylinder (use π ≈ 3.14).

Answer

V = 160\pi \approx 502.4

cm³.

First step

Step 1: Write the formula for the volume of a cylinder:

V = \pi r^2 h

Full solution

2
Step 2: Substitute the values: $V = \pi \times 4^2 \times 10 = \pi \times 16 \times 10 = 160\pi$ .
3
Step 3: Approximate: $V \approx 160 \times 3.14 = 502.4$ cm³.

The volume of a cylinder is the area of the circular base (

\pi r^2

) multiplied by the height (

h

). This formula makes intuitive sense: you are stacking up infinitely many thin circular disks of area

\pi r^2

to a total height

h

Example 2

medium

A cylindrical water tank holds

2000\pi

liters. Its height is 20 m. Find the radius of the tank.

Volume = 2000π. Find radius r.

Example 3

medium

A cylindrical mug has diameter

8

cm and height

10

cm. How many cm³ does it hold (use

\pi\approx 3.14

Example 4

medium

A cylinder has radius

4

and height

h

. Its volume equals

80\pi

. Find

h

Volume = 80π. Find h.

Example 5

medium

Water in a cylinder of radius

3

has depth

8

. The water is poured into an empty cylinder of radius

4

. Find the new depth.

Example 6

hard

A hollow cylindrical pipe has outer radius

5

, inner radius

4

, and length

20

. Find the volume of material.

Example 7

hard

A rectangle with sides

6

and

10

is rolled into a cylinder by joining the two sides of length

10

. Find the volume of the resulting cylinder (no top or bottom).

Example 8

challenge

A cylinder is inscribed in a sphere of radius

5

with the cylinder's axis through the sphere's center. Find the height that maximizes volume, and give that volume in terms of

\pi

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A soup can has a diameter of 8 cm and a height of 12 cm. Find the volume. Leave your answer in terms of

\pi

Find the volume in terms of π.

Example 2

hard

Two cylinders have the same volume. Cylinder A has radius 3 and height 16. Cylinder B has height 4. Find the radius of Cylinder B.

Example 3

easy

A cylinder has radius

5

and height

6

. Find its volume in terms of

\pi

Find the volume in terms of π.

Example 4

easy

A cylinder has diameter

10

and height

7

. Find its volume in terms of

\pi

Diameter

Example 5

easy

Find the volume of a cylinder with radius

2

cm and height

11

cm. Use

\pi\approx 3.14

Find the volume. Use π ≈ 3.14.

Example 6

medium

A cylinder has volume

98\pi

and radius

7

. Find its height.

Volume

Example 7

medium

A cylinder has volume

108\pi

and height

3

. Find its radius.

Volume

Example 8

medium

A water bottle is a cylinder with radius

3

cm and height

20

cm. How many milliliters does it hold? (

1\text{ cm}^3=1\text{ mL}

, use

\pi\approx 3.14

Example 9

medium

A pool is a cylinder with radius

5

m and depth

2

m. How many cubic meters of water does it hold? Leave answer in terms of

\pi

Find the volume in terms of π.

Example 10

medium

A cylinder of radius

4

and height

9

is melted and recast into a cylinder of radius

6

. Find the new height.

Example 11

hard

A cylindrical silo has volume

1000\pi

m³ and height

10

m. Find its diameter.

Volume

Example 12

hard

A cylindrical tank of radius

2

m is being filled at

4\pi

m³/min. How fast (in m/min) does the water level rise?

Example 13

hard

Two cylinders have equal volumes. Cylinder A has radius

4

and height

9

. Cylinder B has radius

6

. Find Cylinder B's height.

Cylinder A: r = 4, h = 9. Cylinder B: r = 6, h = ?

← Back to Volume of a Cylinder Formula Explained Practice Mode

Related Concepts

Area of a Circle Volume Volume of a Cone Surface Area of a Cylinder Volume of a Sphere

Background Knowledge

These ideas may be useful before you work through the harder examples.

area of circlevolume